Interactive simulation of power grid dynamics.

For instructions on how to interact with the simulation, please scroll to the bottom.
Click on the CoNDynNet logo above to return to the main page.

What do we see here?

To the right you see a representation of the Scandinavian high-voltage
power transmission network. The links are existing transmission lines of
capacity K. They change their width proportional to line loading.
The nodes are sites of power producers or consumers, each of which generates
or consumes one unit of power P. The state of each node is
characterised by two variables, its phase φ (node colour) and
frequency ω (node size). The normal operation corresponds to
the synchronisation of all nodes to a common frequency of 50Hz
with constant phase differences such that line loadings are constant.

The phase and frequency of the i-th node, evolve according to the following equation:

The parameter α corresponds to the damping at each node.
You can use the input form to vary it between 0 and 1 (this resets the
simulation). For convenience, the simulation is using a co-rotating
reference frame with a default speed of 50Hz.
You can control the speed in the input form. By setting
it to 50Hz, oscillations at the synchronous grid frequency appear static.
A value of 0Hz then corresponds to a static frame.

The Frequency Meter

In an AC power grid, it is an essential objective to maintain a stable common grid frequency,
typically 50Hz. It corresponds to a perfectly balanced system where electricity production
meets the demand on the consumer side. According to European regulation, frequency deviations
must not be larger than +/-0.2Hz, otherwise special action is required.
To the lower right you see an indicator for the average grid frequency -- a frequency meter.
The needle points upwards when the system operates at 50Hz. Negative and positive deviations
correspond to under- respectively overproduction. The red dots mark the lowest and
highest local frequency deviations, the numerical values are stated below the meter.

Experiments with Local Disturbances

You can now study the effects of disturbances at single nodes on the power grid.
By clicking on a node, its phase φ and frequency ω are reset to values
you can specify in the input form to the right. Set the phase pertubation
to a value between +/-π and the frequency perturbation to a value
between +/-15Hz.
Observe how the nodes change their colour/ size and how the links change their width
proportional to the phase/frequency and line loadings.
Using such experiments, the CoNDyNet researchers attempt to answer questions like:

What is the probability to come back to a stable situation after a local perturbation?

What is the probability that all frequency deviations are strictly limited?

Can we use properties of the network structure to identify the most critical nodes in terms of the above questions?

Controlling the Simulation

There are four coulored buttons on the right to

reset the simulation to a stable operating state.

start/stop a simulation.

reset the phase and frequency of each node (see below) to a random value.

Furthermore, there are two additional buttons to switch the node colour scheme and
to enable a magnifying lens to take a closer look at the netweork.

Related CoNDyNet Publications

Deciphering the imprint of topology on nonlinear dynamical network stability